If both roots of the equation x2−2(a−1)x+(2a+1)=0 are positive. Then following conditions must be true(i) D≥0 (ii) 2(a−1)>0 (iii) 2a+1>0 Case I D=(−2(a−1))2−4(2a+1)≥0 4(a2−2a+1)−4(2a+1)≥0 a2−4a≥0 a(a−4)≥0 a∈(−∞,0]∪[4,∞) .........(i) Case II 2(a−1)>0 a>1 a∈(1,∞) ........(ii) Case III 2a+1>0 a>
−1
2
.........(iii) From Eqs. (i), (ii) and (iii), we get, a∈[4,∞)
